On my first Spring visit to the Woodland/Heath walk I frequent at this time of year, I was able to watch this female Brimstone laying her eggs on a Buckthorn bush. I was talking to a Butterfly Expert at the time who was able to advise on the subject (Thanks Steve).
The Brimstone lays her eggs singularly on leaves on the tips of branches.
Look at the first image below and you can just see the small bottle shaped egg.
Below a much closer shot of the egg.
Later I was able to track a pair of Brimstone during their preparatory flight chase sequence before mating.